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2016-04-05 Nonlinear Seminar

Albert Kubzdela
On some properties of some measure of non-compactness in non-Archimedean analysis

Let $$  \mathbb{K}  $$ be a locally compact non-Archimedean field, and $$  E  $$ a non-Archimedean Banach space over $$  \mathbb{K}  $$. We define non-Archimedean equivalents of several well-known measures of non-compactness defined on $$  E  $$, we describe their properties and we present quantitative versions of several classic statements on weak compactness (theorems of Krein, Gantmacher and Grothendieck) for non-Archimedean Banach spaces.